The \(L_p\) -spaces of \(n_\theta \)  are special instances of noncommutative \(L_p\)  spaces associated with a semi-finite faithful normal trace on a von Neumann algebra [1]}, [2]} (see also [3]}, [4]}). We refer to [3]}, [1]} for the main background on noncommutative \(L_p\) -spaces needed in this paper.
